Violate the principle of relativity?

1. The problem statement, all variables and given/known data
In a water pipe, the light moves in the same direction of the water flow. It is
determined that the speed of light is dependent on the speed of water flow. Does
that violate the principle of relativity?

2. Relevant equations

3. The attempt at a solution
why the speed of light is dependent?
I know it should not be violate the principle of relativity but I don't know how to explain.

A distinction must be made between "speed of light (in a given medium)" and "speed of light in a vacuum (the speed limit of the universe)". I call the latter the "information speed limit".

I can suggest some more if you want, but that nugget of info above may be useful to you :).

EDIT: Actually, that is a downright awful attempt at being helpful, let's see if I can do better. You need to know about velocity addition formulae to answer the question. If you have tried all of that to no avail, then the water stuff is known as the fizeau experiment (books and interwebs know all about it)

In a water pipe, the light moves in the same direction of the water flow. It is determined that the speed of light is dependent on the speed of water flow. Does that violate the principle of relativity?

Hi tkm2002!

No, it confirms the principle of relativity …

the v(1 ± 1/n2) formula is what special relativity predicts (by adding or subtracting v, the speed of the water, to c/n, the speed of light in the water) …